Question

(\(\frac{x}{x+1}\)+1):(1-\(\frac{3x^2}{1-x^2}\))

Answer 1

\(\left(\frac{x}{x+1}+1\right):\left(1-\frac{3x^2}{1-x^2}\right)\)

= \(\left(\frac{x+x+1}{x+1}\right):\left(\frac{1-x^2-3x^2}{\left(1-x\right)\left(1+x\right)}\right)\)

= \(\left(\frac{2x+1}{x+1}\right):\left(\frac{1-4x^2}{\left(1-x\right)\left(1+x\right)}\right)\)

= \(\left(\frac{2x+1}{x+1}\right):\left(\frac{\left(1-2x\right)\left(2x+1\right)}{\left(1-x\right)\left(x+1\right)}\right)\)

= \(\frac{2x+1}{x+1}:\frac{2x+1}{x+1}:\frac{1-2x}{1-x}\)

= \(\frac{1-x}{1-2x}\)

Chúc bn học tốt!!

Answer 2

\(=\left(\frac{x+x+1}{x+1}\right):\left(\frac{1-x^2-3x^2}{1-x^2}\right)\)

\(=\frac{2x+1}{x+1}:\frac{1-4x^2}{\left(1-x\right)\left(1+x\right)}\)

\(=\frac{2x+1}{x+1}\times\frac{\left(1-x\right)\left(1+x\right)}{\left(1-2x\right)\left(1+2x\right)}\)

= \(\frac{1-x}{1-2x}\)

(đkxđ: \(x\ne\pm1,x\ne\pm\frac{1}{2}\))